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Number of complete triangulations of the Koch chain K_s.
2

%I #6 Apr 28 2022 13:16:28

%S 1,1,2,424,975419632,86131212354640695306944,

%T 19668281895304112711343831241714273736245631706515584

%N Number of complete triangulations of the Koch chain K_s.

%C The Koch chain K_s is a sequence of 2^s+1 points which form an x-monotone chain of unavoidable edges in the plane with the same combinatorial structure as the fractal Koch curve.

%C Given that the number of points already grows exponentially in s, the numbers of triangulations themselves have double exponential growth of roughly 9.083^(2^s), see Theorem 5 of Rutschmann, Wettstein (2022).

%D D. Rutschmann and M. Wettstein, "Chains, Koch Chains, and Point Sets with many Triangulations", 38th International Symposium on Computational Geometry (SOCG 2022), to appear.

%H D. Rutschmann and M. Wettstein, <a href="https://arxiv.org/abs/2203.07584">Chains, Koch Chains, and Point Sets with many Triangulations</a>, arXiv preprint arXiv:2203.07584 [cs.CG], 2022.

%Y Product of A352496 and A352497.

%K nonn

%O 0,3

%A _Manuel Wettstein_, Mar 18 2022